In [20] the connections between the Schur algorithm, the Wall’s continued fractions and the orthogonal polynomials are revisited and used to establish some nice convergence properties of the sequence of Schur functions associated with a Schur function. In this report, we generalize some of Krushchev’s results to the case of a multipoint Schur algorithm, that is a Schur algorithm where all the i...

In this paper we will give the character table of the irreducible rational representations of G=SL (2, q) where q= , p prime, n>O, by using the character table and the Schur indices of SL(2,q).

We prove a Murnaghan–Nakayama rule for k-Schur functions of Lapointe and Morse. That is, we give an explicit formula for the expansion of the product of a power sum symmetric function and a k-Schur function in terms of k-Schur functions. This is proved using the noncommutative k-Schur functions in terms of the nilCoxeter algebra introduced by Lam and the affine analogue of noncommutative symmet...

Some new relations on skew Schur function differences are established both combinatorially using Schützenberger’s jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences of skew Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions confirms the validi...

To each partition λ, we introduce a measure Sλ(x; t)sλ(y)/Zt where sλ is the Schur function and Sλ(x; t) is a generalization of the Schur function defined in [M] and Zt is a normalization constant. This measure, which we call the t-Schur measure, is a generalization of the Schur measure [O] and the shifted Schur measure studied by Tracy and Widom [TW3]. We prove that by a certain specialization...

Young’s lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young...

Given a domain $\Omega$ in $\mathbb{C}^n$ and collection of test functions $\Psi$ on $\Omega$, we consider the complex-valued $\Psi$-Schur-Agler class associated to pair $(\Omega,\,\Psi)$. In this article, characterize interpolating sequences for Banach algebra which is closed unit ball. When disc $\mathbb{D}$ complex plane $\mathbb{C}$ function includes only identity $\mathbb{D}$, aforemention...

In their 2011 paper on the AGT conjecture, Alba, Fateev, Litvinov and Tarnopolsky (AFLT) obtained a closed-form evaluation for Selberg integral over product of two Jack polynomials, thereby unifying well-known Kadell Hua--Kadell integrals. this we use variety symmetric functions function techniques to prove generalisations AFLT integral. These include (i) an $\mathrm{A}_n$ analogue integral, co...